“The relation between 4D N=4 SYM and the 6D (2, 0) theory is just like that between Darth Vader and the Emperor. You see Darth Vader and you think “Isn’t he just great? How can anyone be greater than that? No way’.Then you meet the Emperor”. - Nima
It all comes down to the distinction between string theory and M theory. Instead of thinking about the worldvolume theory of a short stack of D3 branes, you know think about stacked M5 branes compactified on a torus. Since we are compactifying on a torus, that most BORING of all the Calabi-Yaus, we keep all that nice supersymmetry. It explains S duality nicely as the mapping class group of the torus. If we compactify on a general Riemann surface, we get other S-duality groups corresponding to that surface.
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